Publisher’s description: To study the structure of a topological algebra, it is useful to know the description of the closed ideals in that topological algebra. In particular, it is important to know which maximal ideals are closed. One of the simplest topological algebras is the algebra of continuous functions on a compact Hausdorff space with the uniform topology. Closed ideals in that commutative topological algebra were described in the first half of the previous century. After that, closed maximal ideals are described in many other topological algebras. Ideals in the topological algebra of continuous sections, defined by a family of general topological algebras, are considered in the present Thesis. In case the family of topological algebras is indexed by a completely regular Hausdorff space, the description of all closed and closed maximal one-sided ideals is obtained. In case the family is indexed by all two-sided ideals of a topological algebra A, conditions when A is densely embedded in that topological algebra of continuous sections are given. In addition, A is densely embedded in a certain topological algebra of continuous maps. In case the indexes are the primitive ideals, defined by the closed maximal regular left (right) ideals of a topological algebra A, the description of all closed maximal regular one-sided ideals of A is obtained. As an application of these results, the descriptions of the left and right topological Jacobson radical are given, which are used to find the conditions when these radicals coincide, partly solving the problem posed by B. Yood in 1964.